Skip to main content

Even Linear Simple Matrix Languages: Formal Language Aspects

  • Conference paper
Combinatorics, Computability and Logic

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

  • 195 Accesses

Abstract

We investigate formal language properties of even linear simple matrix languages and related language classes. More precisely, we discuss characterizations, (proper) inclusion relations, closure properties and decidability questions. In another paper [4], we showed the importance of these language classes for grammatical inference issues.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. J. Berstel. Transductions and Context-Free Languages. Stuttgart: Teubner, 1979.

    MATH  Google Scholar 

  2. J. A. Brzozowski. Regular-like expressions for some irregular languages. In 9th IEEE SWAT (FOCS), pages 278–280, 1968.

    Google Scholar 

  3. J. Dassow and Gh. Păun. Regulated Rewriting in Formal Language Theory, vol. 18 of EATCS Monographs in Theoretical Computer Science. Berlin: Springer, 1989.

    Google Scholar 

  4. H. Fernau. Efficient learning of some linear matrix languages. In 5th COCOON, vol. 1627 of LNCS, pages 221–230, 1999. Extended version as Technical Report WSI-2000–9, Universität Tübingen (Germany), Wilhelm-Schickard-Institut für Informatik.

    Google Scholar 

  5. H. Fernau and J. M. Sempere. Permutations and control sets for learning non-regular language families. In 5th ICGI, vol. 1891 of LNCS/LNAI, pages 75–88, 2000.

    Google Scholar 

  6. S. Ginsburg and E. H. Spanier. Control sets on grammars. Mathematical Systems Theory, 2: 159–177, 1968.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Greibach. Comments on universal and left universal grammars, context-sensitive languages, and context-free grammar forms. Information and Control, 39: 135–142, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Hirose and M. Nasu. Left universal context-free grammars and homomorphic characterizations of languages. Information and Control, 50: 110–118, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  9. N. A. Khabbaz. A geometric hierarchy of languages. Journal of Computer and System Sciences, 8: 142–157, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Mäkinen. A note on the grammatical inference problem for even linear languages. Fundamenta Informaticae, 25: 175–181, 1996.

    MathSciNet  MATH  Google Scholar 

  11. C. Martín-Vide. Natural language understanding: a new challenge for grammar systems. Acta Cybernetica, 12: 461–472, 1996.

    MATH  Google Scholar 

  12. A. Mateescu. Special families of matrix languages and decidable problems. Acta Cybernetica, 10: 45–52, 1991.

    MathSciNet  MATH  Google Scholar 

  13. H. Maurer and W. Kuich. Tuple languages. In Proc. of the ACM International Computing Symposium, pages 882–891, 1970.

    Google Scholar 

  14. Gh. Păun. Linear simple matrix languages. Elektronische Informationsverarbeitung and Kybernetik (EIK), 14: 377–384, 1978.

    MATH  Google Scholar 

  15. J. M. Sempere and P. García. A characterization of even linear languages and its application to the learning problem. In 2nd ICGI, vol. 862 of LNCS/LNAI, pages 38–44, 1994.

    Google Scholar 

  16. R. Siromoney. On equal matrix languages. Information and Control, 14: 133–151, 1969.

    Article  Google Scholar 

  17. Y. Takada. Grammatical inference of even linear languages based on control sets. Information Processing Letters, 28: 193–199, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Takada. Learning even equal matrix languages based on control sets. In ICPIA’92, vol. 652 of LNCS, pages 274–289, 1992.

    Google Scholar 

  19. Y. Takada. A hierarchy of language families learnable by regular language learning. Information and Computation, 123: 138–145, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  20. Y. Takada. Learning formal languages based on control sets. In Algorithmic Learning for Knowledge-Based Systems, vol. 961 of LNCS/LNAI, pages 317–339, 1995.

    Google Scholar 

  21. D. J. Weir. A geometric hierarchy beyond context-free languages. Theoretical Computer Science, 104: 235–261, 1992.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London Limited

About this paper

Cite this paper

Fernau, H. (2001). Even Linear Simple Matrix Languages: Formal Language Aspects. In: Calude, C.S., Dinneen, M.J., Sburlan, S. (eds) Combinatorics, Computability and Logic. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0717-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0717-0_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-526-7

  • Online ISBN: 978-1-4471-0717-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics